X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/blobdiff_plain/fdc11565a5688a74effe8d08b78b4a1853387f3a..dea60eccf9392a4db51bae0ae16bbabc4203facb:/paper.tex

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@@ -746,14 +746,19 @@ This figure show the execution time of the both algorithm EA and DK with sparse
 
 %\subsubsection{The execution time of Ehrlich-Aberth algorithm on OpenMP(1 core, 4 cores) vs. on a Tesla GPU}
 
+\section{Conclusion and perspective}
+\label{sec7}
+In this paper we have presented the parallel implementation Ehrlich-Aberth method on GPU and on CPU (openMP) for the problem of finding roots polynomial. Moreover, we have improved the classical Ehrlich-Aberth method witch suffer of overflow problems, the exp.log solution applying to the iterative function to resolve high degree polynomial.
 
+Then, we have described the parallel implementation of the Ehrlich-Aberth algorithm on GPU. 
+We have performed some experiments on Ehrlich-Aberth algorithm in CPU and GPU from the both sparse and full polynomial. These experiments lead us to conclude that the iterative methods using data-parallel operations are more efficient on the GPU than on the CPU. Moreover, the experiment showed that Ehrlich-Aberth algorithm on GPU converge from the both sparse and full polynomials with precision of $10^{-7}$ and the execution time very faster than the CPU version. 
+The experiences showed that the improvement brought to Ehrlich-Aberth allows to resolve very large degree polynomial exceed 100,000.
+Finally, we have compared Ehrlich-Aberth algorithm to Durand-Kerner algorithm, we have conclude that Ehrlich-Aberth converges more quickly than Durand-Kerner in execution time, it is due in fact that Ehrlich-Aberth has cubic one convergence While Durand-Kerner is quadratic. In counterpart, the execution time per iteration are very low for Durand-Kerner algorithm compare to the Ehrlich-Aberth algorithm, consequently, it need lot of iterations to converge. We have to notice that Durand-Kerner does not converge for full polynomial which exceed 5000 degrees while Ehrlich-Aberth was able to solve full polynomial of degree 500,000.
 
+In future work, we plan to perform some experiments using several GPU with a cluster of GPU. So it is interesting to implement algorithms using at least two forms of parallelism on GPU and CPU.
 
 
 
-\section{Conclusion and perspective}
-
-\label{sec7}
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